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A161434
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Number of 6-compositions.
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2
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1, 6, 57, 524, 4803, 44022, 403495, 3698352, 33898338, 310705224, 2847860436, 26102905368, 239253883390, 2192952083712, 20100149570496, 184233853423936, 1688649759962676, 15477817777932456, 141866507103389516, 1300319342589168000, 11918460722228694720
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OFFSET
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0,2
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COMMENTS
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LINKS
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E. Munarini, M. Poneti, S. Rinaldi, Matrix compositions, Journal of Integer Sequences, Vol. 12 (2009), Article 09.4.8
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FORMULA
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Recurrence: a(n+6) = 12*a(n+5) - 30*a(n+4) + 40*a(n+3) - 30*a(n+2) + 12*a(n+1) - 2*a(n).
G.f.: (1-x)^6/(2*(1-x)^6-1).
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1,
add(a(n-j)*binomial(j+5, 5), j=1..n))
end:
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MATHEMATICA
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Join[{1}, LinearRecurrence[{12, -30, 40, -30, 12, -2}, {6, 57, 524, 4803, 44022, 403495}, 20]] (* Jean-François Alcover, Jan 08 2016 *)
CoefficientList[Series[(1-x)^6/(2*(1-x)^6-1), {x, 0, 50}], x] (* G. C. Greubel, Nov 25 2017 *)
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PROG
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(PARI) x='x+O('x^30); Vec((1-x)^6/(2*(1-x)^6-1)) \\ G. C. Greubel, Nov 25 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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